Graphs of subgroups of free groups

Louder, Larsen; McReynolds, D B

doi:10.2140/agt.2009.9.327

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Graphs of subgroups of free groups

Larsen Louder and D B McReynolds

Algebraic & Geometric Topology 9 (2009) 327–335

DOI: 10.2140/agt.2009.9.327

Abstract

We construct an efficient model for graphs of finitely generated subgroups of free groups. Using this we give a very short proof of Dicks’s reformulation of the strengthened Hanna Neumann Conjecture as the Amalgamated Graph Conjecture. In addition, we answer a question of Culler and Shalen on ranks of intersections in free groups. The latter has also been done independently by R P Kent IV.

Keywords

folding, free groups, Hanna Neumann conjecture

Mathematical Subject Classification 2000

Primary: 20E05

References

Publication

Received: 27 August 2008

Revised: 25 January 2009

Accepted: 28 January 2009

Published: 23 February 2009

Authors

Larsen Louder
Department of Mathematics University of Michigan Ann Arbor, MI 48109-1043 USA
http://www.math.lsa.umich.edu/~llouder/
D B McReynolds
Department of Mathematics University of Chicago Chicago, IL 60637 USA
http://www.math.uchicago.edu/~dmcreyn/

Volume 9, issue 1 (2009)